# How to reverse a sequence in SQL

I wrote an article a while back about how to order updates in MySQL so you don’t violate a unique index. I said I’d write another article on how to swap numbers in a sequence with a unique index. This is that article, but I’m going to make it a little more generic: how to reverse a (possibly ordered) sequence.

I’ve been thinking about this for a while, wondering if there’s a way I can do it in-place in one statement (I like to pile challenge upon difficulty). I’ve thought of a number of techniques, some using one statement, some using more, some that won’t work on MySQL, some that will.

This article assumes a sequence of non-negative numbers in the following table:

create table t (
pk int not null auto_increment primary key,
i int not null,
unique key(i)
);
insert into t(i) values (1), (2), (3), (4), (5);

The pk column is so there’s something to compare the original ordering against, and I will not use it in any query other than to show the original order. I don’t assume the sequence is composed of adjacent numbers – there could be gaps, and they don’t have to be strictly increasing.

### Method 1: in-place, one statement

The most straightforward way to reverse a sequence is to do it in-place, in one statement, with a little subtraction. First, here’s a SELECT statement to reverse the sequence:

select pk, (select min(i) from t) + (select max(i) from t) - i from t;

Given that statement, you can write an UPDATE statement based on it:

update t set i = (select min(i) from t) + (select max(i) from t) - i;

That is valid SQL, and will work on other RDBMSs, but for a number of reasons it won’t work in MySQL. The first problem is “ERROR 1093 (HY000): You can’t specify target table ’t’ for update in FROM clause.” You can solve this with variables:

select @min := min(i) from t;
select @max := max(i) from t;
update t set i = @min + @max - i;

Now you get the unique index violation: “ERROR 1062 (23000): Duplicate entry ‘5′ for key 1.” There’s just no way around this in MySQL. You must turn to more devious methods!

### Method 2: bitwise XOR

Ah, here’s a solution in search of a problem! Let’s see, bitwise XOR is really cool, what can you use it for today?

Well, you can use it to swap some numbers, for starters. As you may know, you can XOR two numbers together three times and they will magically trade places. It’s a great way to swap numbers without using a temporary variable for extra storage, though that’s really of dubious value here. In any case, it’s a fun exercise to write in one statement. Can you do it more simply than the following?

select pk, ((i ^ (@min + @max - i)) ^ ((i ^ (@min + @max - i)) ^ (@min + @max - i))) from t;

Unfortunately, once you’ve proven you can use XOR to reverse the sequence, the problem of assigning it back to t is still the same; you can’t do that in MySQL without violating unique indexes.

### Method 3: mirror, delete and shift

Another method is to copy the sequence back into the table, with an offset so the unique index isn’t violated, then delete the original sequence and shift the copy back into its place (or some variation of this scheme). This will work as long as the column’s data type has enough room to store the copy. In this case, the sequence is non-negative, so negative numbers are a good place to hold the copy.

insert into t(i) select -i from t;
delete from t where i between @min and @max;
update t set i = @max + 1 + i;

This is the first method I’ve shown that will work on MySQL. Other variations on this method include copying the rows off to a temporary table. Regardless, the basic thing that makes this work on MySQL is deleting the entire original sequence before trying to put anything back in its place. If you don’t do that, the index will be violated.

### Other methods

Besides variations on method 3, there are some other creative things you could do:

• Add another column, reverse the sequence into that column, then delete the original column and rename the new.
• Use the XOR technique on only half the table at once: XOR the bottom half against the top, the top against the bottom, and the bottom against the top again. This doesn’t work if there’s a unique index, as in the example I give.
• Use an ORDER BY clause to reverse the numbers. For my examples shown here, this is the obvious solution, but it doesn’t work if the numbers aren’t in increasing order.
• Allow NULLs in the column, then instead of deleting in method 3, just set to NULL temporarily.

### Summary

I just showed you a bunch of different ways to reverse a sequence in SQL, something that may or may not be useful. I’ve been amusing myself for months trying to find fund and different ways to solve this problem. I’m interested in any ideas you have too.

I'm Baron Schwartz, the founder and CEO of VividCortex. I am the author of High Performance MySQL and many open-source tools for performance analysis, monitoring, and system administration. I contribute to various database communities such as Oracle, PostgreSQL, Redis and MongoDB.